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Environment configured for regression analysis.

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Sample size: 6,319 listings
Variables: 13 columns
Price range: £10.00 - £74100.00

Dataset Overview:
   Observations: 6,319
   Variables: 13

Sample preview (first 5 observations):

Note: 64 listings above £1214 excluded from chart for clarity

Average price: £220.48 per night
Median price: £135.00
Cheapest listing: £10.00
Most expensive listing: £74100.00

Note: 64 extreme outliers (>1214£) excluded for clarity

Note: Showing 99% of data (prices ≤ £1214)

Average prices by room type:
  Hotel room: £549.11/night
  Entire home/apt: £281.90/night
  Private room: £85.99/night
  Shared room: £38.84/night

Note: 64 extreme price outliers excluded for clarity

Note: 62 extreme price outliers excluded for clarity

Correlation Interpretation:
  r > 0.7: Strong positive association
  r > 0.3: Moderate positive association
  r < -0.3: Moderate negative association
  |r| < 0.3: Weak or no linear relationship

Geographic Insights:
  Central London (higher density) shows elevated pricing
  Price gradient visible from city center to periphery
  Yellow/light colors = Higher priced listings
  Purple/dark colors = Lower priced listings

Availability Statistics:
  Mean availability: 217 days/year
  Median availability: 248 days/year
  Fully available (365 days): 349 listings (5.5%)
  Not available (0 days): 81 listings (1.3%)

Business Insight: Bimodal distribution suggests full-time vs. occasional hosting strategies

Minimum Nights Statistics:
  Median minimum nights: 2
  1-night stays allowed: 2,336 listings (37.0%)
  Weekly minimum (7+ nights): 762 listings (12.1%)

Business Insight: Longer minimum stays often correlate with lower nightly rates (volume pricing strategy)

Outlier Detection (IQR Method):
  Q1 (25th percentile): £77.00
  Q3 (75th percentile): £223.50
  IQR: £146.50
  Lower bound: £-142.75
  Upper bound: £443.25

  Outliers detected: 457 listings (7.2%)
  Price range of outliers: £444.00 - £74100.00

Missing Values Summary:
   Column  Missing_Count  Missing_Percent
bathrooms             69             1.09
 bedrooms             13             0.21
     beds             13             0.21

Duplicates removed.
Observations after deduplication: 6,319

Duplicate rows found: 0
Total rows before check: 6,319

Logarithmic transformation applied.
Original price range: £10.00 - £74100.00
Transformed range: 2.40 - 11.21

Selected 3 continuous predictors:
  - accommodates
  - bedrooms
  - beds

Added 3 room type variables

Total features for model: 6

Median imputation applied:
  - bedrooms: 13 values imputed
  - beds: 13 values imputed

Analysis dataset prepared.
  Observations: 6,319
  Predictors: 6

Data types validation:
accommodates           int64
bedrooms             float64
beds                 float64
room_Hotel room         bool
room_Private room       bool
room_Shared room        bool
log_price            float64
dtype: object

First observations:
   accommodates  bedrooms  beds  room_Hotel room  room_Private room  \
0             4       1.0   1.0            False              False   
1             5       3.0   3.0            False              False   
2             8       4.0   4.0            False              False   
3             4       2.0   2.0            False              False   
4             6       4.0   2.0            False              False   

   room_Shared room  log_price  
0             False   4.844187  
1             False   5.420535  
2             False   7.783641  
3             False   5.017280  
4             False   5.198497  

Training data prepared.
  Training set: 6,319 observations (100% of data)

Data types in X_train:
accommodates           int64
bedrooms             float64
beds                 float64
room_Hotel room         bool
room_Private room       bool
room_Shared room        bool
dtype: object

Note: Model trained on entire dataset for maximum sample size.

BASELINE MODEL Results:
  Predictors: accommodates, bedrooms
  R² (Coefficient of Determination): 0.3511
  Adjusted R²: 0.3509
  Effect size: Medium (Cohen's f² = 0.541)
  RMSE (Root Mean Squared Error): 0.6474
  Adjusted for predictors: 35.1%

Model Performance:
  Explained variance: 35.1%

FULL MODEL Results:
  Number of predictors: 6
  R² (Coefficient of Determination): 0.5004
  Adjusted R²: 0.4999
  RMSE (Root Mean Squared Error): 0.5681

Model Performance:
  Explained variance: 50.0%
  Adjusted for predictors: 50.0%
  Effect size: Large (Cohen's f² = 1.002)

Model Comparison:
  Incremental variance explained: 14.9%
  ΔR² = 0.1493

Additional predictors provide improvement (ΔR² > 0).

Data prepared: 6319 observations, 6 features
Data types: [dtype('float64')]
================================================================================
STATSMODELS OLS REGRESSION RESULTS
================================================================================
                            OLS Regression Results                            
==============================================================================
Dep. Variable:              log_price   R-squared:                       0.500
Model:                            OLS   Adj. R-squared:                  0.500
Method:                 Least Squares   F-statistic:                     1054.
Date:                Sun, 30 Nov 2025   Prob (F-statistic):               0.00
Time:                        18:38:59   Log-Likelihood:                -5392.9
No. Observations:                6319   AIC:                         1.080e+04
Df Residuals:                    6312   BIC:                         1.085e+04
Df Model:                           6                                         
Covariance Type:            nonrobust                                         
=====================================================================================
                        coef    std err          t      P>|t|      [0.025      0.975]
-------------------------------------------------------------------------------------
const                 4.6250      0.018    252.981      0.000       4.589       4.661
accommodates          0.1122      0.007     16.752      0.000       0.099       0.125
bedrooms              0.1644      0.012     13.828      0.000       0.141       0.188
beds                 -0.0523      0.009     -5.857      0.000      -0.070      -0.035
room_Hotel room       0.8721      0.190      4.595      0.000       0.500       1.244
room_Private room    -0.7310      0.018    -40.994      0.000      -0.766      -0.696
room_Shared room     -1.3692      0.134    -10.244      0.000      -1.631      -1.107
==============================================================================
Omnibus:                     2367.847   Durbin-Watson:                   2.009
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            16823.851
Skew:                           1.618   Prob(JB):                         0.00
Kurtosis:                      10.310   Cond. No.                         134.
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

================================================================================
BUSINESS-FRIENDLY INTERPRETATION OF KEY STATISTICS
================================================================================

TOP 5 PREDICTORS BY ABSOLUTE COEFFICIENT MAGNITUDE:
==================================================
room_Shared room     β = -1.3692 (negative association)
room_Hotel room      β =  0.8721 (positive association)
room_Private room    β = -0.7310 (negative association)
bedrooms             β =  0.1644 (positive association)
accommodates         β =  0.1122 (positive association)

Green bars = positive coefficients
Red bars = negative coefficients

Variance Inflation Factor (VIF) Analysis:
==================================================
          Feature       VIF
     accommodates 11.604452
         bedrooms  9.018756
             beds  8.733639
room_Private room  1.140507
 room_Shared room  1.046276
  room_Hotel room  1.000697

Interpretation:
  VIF < 5: Low multicollinearity (acceptable)
  VIF 5-10: Moderate multicollinearity (caution)
  VIF > 10: High multicollinearity (problematic)

(!) WARNING: 1 predictor(s) exhibit high multicollinearity.

Observations proximate to diagonal indicate accurate predictions.
Deviation from diagonal represents prediction error.

Mean residual: 0.0000
Std deviation: 0.5681

============================================================
MODEL FIT STATISTICS
============================================================

Baseline Model (k=2):
  R² = 0.3511
  Adjusted R² = 0.3509
  RMSE = 0.6474

Full Model (k=6):
  R² = 0.5004
  Adjusted R² = 0.4999
  RMSE = 0.5681

Model Comparison:
  ΔR² = 0.1493
  ΔAdjusted R² = 0.1490

Conclusion:
  Full model justified: Adjusted R² improvement = 14.90%

Average error: 0.0000
Typical error size: 0.4100

Good residuals should be randomly scattered around zero!

Prediction Accuracy Summary:
  Exact category match: 55.8%
  Within one category: 97.8%

Diagonal = correct predictions (darker = more accurate)
Off-diagonal = misclassifications